Add-Member : Cannot add a member with the name "ComputerName" because a member with that name already exists. If you want to overwrite the member anyway, use the Force parameter to overwrite it.
At line:3 char:22
+ $Obj | Add-Member < <<< -MemberType NoteProperty -Name "ComputerName" -Value $C
+ CategoryInfo : InvalidOperation: (@{ComputerName=Computer1}:PSObject) [Add-Member], InvalidOperationException
+ FullyQualifiedErrorId : MemberAlreadyExists,Microsoft.PowerShell.Commands.AddMemberCommand
Add-Member : Cannot add a member with the name "ComputerName" because a member with that name already exists. If you want to overwrite the member anyway, use the Force parameter to overwrite it.
At line:3 char:22
+ $Obj | Add-Member <<<< -MemberType NoteProperty -Name "ComputerName" -Value $C
+ CategoryInfo : InvalidOperation: (@{ComputerName=Computer1}:PSObject) [Add-Member], InvalidOperationException
+ FullyQualifiedErrorId : MemberAlreadyExists,Microsoft.PowerShell.Commands.AddMemberCommand

In the output you've described, that's what you'd get if you had three different objects, each one with a ComputerName property, rather than one object with a ComputerName property containing three values. That code might look something like this: